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Consequent
A consequent is the second half of a hypothetical proposition. In the standard form of such a proposition, it is the part that follows "then". In an implication, if ''P'' implies ''Q'', then ''P'' is called the antecedent and ''Q'' is called the consequent. In some contexts, the consequent is called the ''apodosis''.See Conditional sentence. Examples: * If P, then Q. Q is the consequent of this hypothetical proposition. * If X is a mammal, then X is an animal. Here, "X is an animal" is the consequent. * If computers can think, then they are alive. "They are alive" is the consequent. The consequent in a hypothetical proposition is not necessarily a consequence of the antecedent. * If monkeys are purple, then fish speak Klingon. "Fish speak Klingon" is the consequent here, but intuitively is not a consequence of (nor does it have anything to do with) the claim made in the antecedent that "monkeys are purple. See also * Antecedent (logic) * Conjecture In mathematic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Conditional Sentence
Conditional sentences are natural language sentences that express that one thing is contingent on something else, e.g. "If it rains, the picnic will be cancelled." They are so called because the impact of the main clause of the sentence is ''conditional'' on the dependent clause. A full conditional thus contains two clauses: a dependent clause called the ''antecedent'' (or ''protasis'' or ''if-clause''), which expresses the condition, and a main clause called the ''consequent'' (or ''apodosis'' or ''then-clause'') expressing the result. Languages use a variety of grammatical forms and constructions in conditional sentences. The forms of verbs used in the antecedent and consequent are often subject to particular rules as regards their tense, aspect, and mood. Many languages have a specialized type of verb form called the conditional mood – broadly equivalent in meaning to the English "would (do something)" – for use in some types of conditional sentences. Types of conditio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Antecedent (logic)
An antecedent is the first half of a hypothetical proposition, whenever the if-clause precedes the then-clause. In some contexts the antecedent is called the ''protasis''. Examples: * If P, then Q. This is a nonlogical formulation of a hypothetical proposition. In this case, the antecedent is P, and the consequent is Q. In an implication, if \phi implies \psi then \phi is called the antecedent and \psi is called the consequent.Sets, Functions and Logic - An Introduction to Abstract Mathematics, Keith Devlin, Chapman & Hall/CRC Mathematics, 3rd ed., 2004 Antecedent and consequent are connected via logical connective to form a proposition In logic and linguistics, a proposition is the meaning of a declarative sentence. In philosophy, " meaning" is understood to be a non-linguistic entity which is shared by all sentences with the same meaning. Equivalently, a proposition is the no .... * If X is a man, then X is mortal. "X is a man" is the antecedent for this proposition. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Material Conditional
The material conditional (also known as material implication) is an operation commonly used in logic. When the conditional symbol \rightarrow is interpreted as material implication, a formula P \rightarrow Q is true unless P is true and Q is false. Material implication can also be characterized inferentially by modus ponens, modus tollens, conditional proof, and classical reductio ad absurdum. Material implication is used in all the basic systems of classical logic as well as some nonclassical logics. It is assumed as a model of correct conditional reasoning within mathematics and serves as the basis for commands in many programming languages. However, many logics replace material implication with other operators such as the strict conditional and the variably strict conditional. Due to the paradoxes of material implication and related problems, material implication is not generally considered a viable analysis of conditional sentences in natural language. Notati ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Necessity And Sufficiency
In logic and mathematics, necessity and sufficiency are terms used to describe a conditional or implicational relationship between two statements. For example, in the conditional statement: "If then ", is necessary for , because the truth of is guaranteed by the truth of (equivalently, it is impossible to have without ). Similarly, is sufficient for , because being true always implies that is true, but not being true does not always imply that is not true. In general, a necessary condition is one that must be present in order for another condition to occur, while a sufficient condition is one that produces the said condition. The assertion that a statement is a "necessary ''and'' sufficient" condition of another means that the former statement is true if and only if the latter is true. That is, the two statements must be either simultaneously true, or simultaneously false. In ordinary English (also natural language) "necessary" and "sufficient" indicate relations betw ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Conditionals
Conditional (if then) may refer to: *Causal conditional, if X then Y, where X is a cause of Y *Conditional probability, the probability of an event A given that another event B has occurred *Conditional proof, in logic: a proof that asserts a conditional, and proves that the antecedent leads to the consequent *Strict conditional, in philosophy, logic, and mathematics *Material conditional, in propositional calculus, or logical calculus in mathematics * Relevance conditional, in relevance logic *Conditional (computer programming), a statement or expression in computer programming languages *A conditional expression in computer programming languages such as ?: *Conditions in a contract Grammar and linguistics *Conditional mood (or conditional tense), a verb form in many languages *Conditional sentence, a sentence type used to refer to hypothetical situations and their consequences **Indicative conditional, a conditional sentence expressing "if A then B" in a natural language **Cou ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Proposition
In logic and linguistics, a proposition is the meaning of a declarative sentence. In philosophy, " meaning" is understood to be a non-linguistic entity which is shared by all sentences with the same meaning. Equivalently, a proposition is the non-linguistic bearer of truth or falsity which makes any sentence that expresses it either true or false. While the term "proposition" may sometimes be used in everyday language to refer to a linguistic statement which can be either true or false, the technical philosophical term, which differs from the mathematical usage, refers exclusively to the non-linguistic meaning behind the statement. The term is often used very broadly and can also refer to various related concepts, both in the history of philosophy and in contemporary analytic philosophy. It can generally be used to refer to some or all of the following: The primary bearers of truth values (such as "true" and "false"); the objects of belief and other propositional attitudes (i. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Conjecture
In mathematics, a conjecture is a conclusion or a proposition that is proffered on a tentative basis without proof. Some conjectures, such as the Riemann hypothesis (still a conjecture) or Fermat's Last Theorem (a conjecture until proven in 1995 by Andrew Wiles), have shaped much of mathematical history as new areas of mathematics are developed in order to prove them. Important examples Fermat's Last Theorem In number theory, Fermat's Last Theorem (sometimes called Fermat's conjecture, especially in older texts) states that no three positive integers a, ''b'', and ''c'' can satisfy the equation ''a^n + b^n = c^n'' for any integer value of ''n'' greater than two. This theorem was first conjectured by Pierre de Fermat in 1637 in the margin of a copy of '' Arithmetica'', where he claimed that he had a proof that was too large to fit in the margin. The first successful proof was released in 1994 by Andrew Wiles, and formally published in 1995, after 358 years of effort by ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
